拓扑递推中 x-y$ 交映变换公式的拉普拉斯变换

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-24 DOI:10.4310/cntp.2023.v17.n4.a1

Alexander Hock

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引用次数: 0

摘要

来自拓扑递归的 $x-y$ 交映变换的函数关系有很多应用；例如，它是自由概率中的高阶矩积关系，或可用于计算复曲线模空间上的交点数。我们推导了这一函数关系的拉普拉斯变换，它作为$\hbar$中的形式幂级数，具有非常漂亮和紧凑的形式。我们将拉普拉斯变换公式应用于艾里曲线和兰伯特曲线，从而为 $\psi$ 级交点数和 $\overline{mathcal{M}}_{g,n}$ 上的霍奇积分提供了简单的公式。

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Laplace transform of the $x-y$ symplectic transformation formula in Topological Recursion

The functional relation coming from the $x-y$ symplectic transformation of Topological Recursion has a lot of applications; for instance it is the higher order moment-cumulant relation in free probability or can be used to compute intersection numbers on the moduli space of complex curves. We derive the Laplace transform of this functional relation, which has a very nice and compact form as a formal power series in $\hbar$. We apply the Laplace transformed formula to the Airy curve and the Lambert curve which provides simple formulas for $\psi$-class intersections numbers and Hodge integrals on $\overline{\mathcal{M}}_{g,n}$.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.